Escape rate of Brownian particles from a metastable potential well under time derivative Ornstein-Uhlenbeck noise

We investigate the escape rate of Brownian particles that move in a cubic metastablepotential subjected to an internal time derivative Ornstein-Uhlenbeck noise (DOUN). Thisnoise can induce the ballistic diffusion of force-free Brownian particles. Some newfeatures are found. The escape rate for DOUN shows qualitative different dependence onpotential well width compared with OUN which induces normal diffusion. As the potentialbarrier height decreases, the escape rate of DOUN deviates from Arrhenius law considerablyearlier than that of Ornstein-Uhlenbeck noise (OUN). The Brownian particles escape fasterunder DOUN than that under OUN. A quasi-periodic oscillation occurs in transient state. Asolvable case is presented to demonstrate the significant cancellation behavior in thebarrier region that governs most of these phenomena. The physical mechanism of thefindings can be clarified by the noise features. These characteristics should be commonfor internal noises that induce superdiffusion, especially the ballistic diffusion.